let S be non empty partial quasi_total non-empty Group-like invariant TRSStr ; :: thesis: for a being Element of S st S is (R2) & S is (R9) holds
a * (a ") <<>> 1. S
let a be Element of S; :: thesis: ( S is (R2) & S is (R9) implies a * (a ") <<>> 1. S )
assume A1: ( S is (R2) & S is (R9) ) ; :: thesis: a * (a ") <<>> 1. S
take ((a ") ") * (a ") ; :: according to ABSRED_0:def 20 :: thesis: ( a * (a ") <=*= ((a ") ") * (a ") & ((a ") ") * (a ") =*=> 1. S )
(a ") " ==> a by A1;
hence ((a ") ") * (a ") =*=> a * (a ") by Th2, ThI2; :: thesis: ((a ") ") * (a ") =*=> 1. S
thus ((a ") ") * (a ") =*=> 1. S by A1, Th2; :: thesis: verum